reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem Th30:
  n > 0 implies n in dom (Newton_Coeff n)
  proof
    assume n>0; then
    A1: n in Seg n by FINSEQ_1:3;
    dom (Newton_Coeff n) = Seg (len (Newton_Coeff n)) by FINSEQ_1:def 3
    .= Seg (n+1) by NEWTON:def 5;
    hence thesis by A1,FINSEQ_2:8;
  end;
